ANOMALOUS BEHAVIOR OF IDEAL FERMI GAS BELOW 2D: THE "IDEAL QUANTUM DOT" AND THE PAUL EXCLUSION PRINCIPLE

2009 ◽  
Author(s):  
M. GRETHER ◽  
M. DE LLANO ◽  
M. HOWARD LEE
Keyword(s):  
Quantum Dot ◽  
Fermi Gas ◽  
Anomalous Behavior ◽  
Exclusion Principle ◽  
Ideal Quantum ◽  
The Ideal

ANOMALOUS BEHAVIOR OF IDEAL FERMI GAS BELOW 2D: THE "IDEAL QUANTUM DOT" AND THE PAUL EXCLUSION PRINCIPLE

2009 ◽  
Vol 23 (20n21) ◽  
pp. 4121-4128 ◽  
Author(s):  
M. GRETHER ◽  
M. DE LLANO ◽  
M. HOWARD LEE
Keyword(s):  
Quantum Dot ◽  
Chemical Potential ◽  
Pauli Exclusion Principle ◽  
Fermi Gas ◽  
Anomalous Behavior ◽  
Absolute Temperature ◽  
Exclusion Principle ◽  
Ideal Quantum ◽  
Spatial Dimensionality ◽  
The Ideal

A physical interpretation is given to a curious "hump" that develops in the chemical potential as a function of absolute temperature in an ideal Fermi gas for any spatial dimensionality d < 2, integer or not, in contrast with the more familiar monotonic decrease for all d ≥ 2. The hump height increases without limit as d decreases to zero. The divergence at d = 0 is shown to be a clear manifestation of the Pauli Exclusion Principle whereby two spinless fermions cannot sit on top of each other in configuration space. The hump itself is thus an obvious precursor of this manifestation, otherwise well understood in momentum space. It also constitutes an "ideal quantum dot" when d = 0.

scholarly journals Fermi gas approach to general rank theories and quantum curves

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Naotaka Kubo
Keyword(s):  
Matrix Models ◽  
Critical Role ◽  
Three Dimensional ◽  
Fermi Gas ◽  
Fermi Gases ◽  
Partition Functions ◽  
Density Matrices ◽  
General Rank ◽  
Chern Simons ◽  
The Ideal

Abstract It is known that matrix models computing the partition functions of three-dimensional $$ \mathcal{N} $$ N = 4 superconformal Chern-Simons theories described by circular quiver diagrams can be written as the partition functions of ideal Fermi gases when all the nodes have equal ranks. We extend this approach to rank deformed theories. The resulting matrix models factorize into factors depending only on the relative ranks in addition to the Fermi gas factors. We find that this factorization plays a critical role in showing the equality of the partition functions of dual theories related by the Hanany-Witten transition. Furthermore, we show that the inverses of the density matrices of the ideal Fermi gases can be simplified and regarded as quantum curves as in the case without rank deformations. We also comment on four nodes theories using our results.

Finite-size effects in the ideal Fermi gas

1989 ◽  
Vol 22 (11) ◽  
pp. L489-L496 ◽  
Author(s):  
V Subrahmanyam ◽  
M Barma
Keyword(s):  
Size Effects ◽  
Finite Size ◽  
Fermi Gas ◽  
Finite Size Effects ◽  
The Ideal

Optical demonstrations of statistical decision theory for quantum systems

2004 ◽  
Vol 4 (6&7) ◽  
pp. 450-459
Author(s):  
S.M. Barnett
Keyword(s):  
Information Theory ◽  
Communication Systems ◽  
Quantum Information Theory ◽  
Quantum Systems ◽  
Quantum Limit ◽  
Statistical Decision Theory ◽  
Statistical Decision ◽  
Ideal Quantum ◽  
Optical Polarisation ◽  
The Ideal

The work of Holevo and other pioneers of quantum information theory has given us limits on the performance of communication systems. Only recently, however, have we been able to perform laboratory demonstrations approaching the ideal quantum limit. This article presents some of the known limits and bounds together with the results of our experiments based on optical polarisation.

Fermi–Dirac Statistics

2019 ◽  
pp. 386-403
Author(s):  
Robert H. Swendsen
Keyword(s):  
High Temperature ◽  
Low Temperature ◽  
Specific Heat ◽  
Fermi Energy ◽  
Fermi Gas ◽  
Main Application ◽  
Densities Of States ◽  
Low Temperature Specific Heat ◽  
Very High ◽  
The Ideal

The main application of Fermi–Dirac Statistics is to calculate the properties of electrons. This chapter explains how the properties of fermions account for the behavior of metals. The Fermi energy is introduced and shown to correspond to a very high temperature, so that most properties can be obtained from low-temperature expansions. Both discrete and continuous densities of states are discussed. The Sommerfeld expansion is derived explicitly. The low-temperature specific heat and compressibility are derived. The most important fermions are electrons, and understanding the properties of electrons is central to understanding the properties of all materials. In this chapter we will study the ideal Fermi gas, which turns out to explain many of the properties of electrons in metals.

PRESSURE COMPARISON BETWEEN THE SPHERICAL CELLULAR MODEL AND THE THOMAS-FERMI MODEL

2007 ◽  
Vol 21 (13n14) ◽  
pp. 2045-2054 ◽  
Author(s):  
GEORGE A. BAKER
Keyword(s):  
Fermi Gas ◽  
Ideal Gas ◽  
The Other ◽  
Cellular Model ◽  
Fermi Model ◽  
Thomas Fermi ◽  
Other Hand ◽  
The Ideal

The widely used Thomas Fermi model always produces pressure which is less than or equal to that of the ideal Fermi gas. On the other hand the spherical cellular model, in certain regions of the temperature-density plane, can produce pressures which are greater than that of the ideal gas. This phenomenon is investigated.

IDEAL QUANTUM READING OF OPTICAL MEMORIES

2012 ◽  
Vol 10 (08) ◽  
pp. 1241010 ◽  
Author(s):  
MICHELE DALL'ARNO ◽  
ALESSANDRO BISIO ◽  
GIACOMO MAURO D'ARIANO
Keyword(s):  
Optical Memory ◽  
Optimal Strategies ◽  
High Accuracy ◽  
Classical Information ◽  
Minimal Error ◽  
Quantum Properties ◽  
Optical Memories ◽  
Ideal Quantum ◽  
Perfect Discrimination ◽  
The Ideal

Quantum reading is the art of exploiting the quantum properties of light to retrieve classical information stored in an optical memory with low energy and high accuracy. Focusing on the ideal scenario where noise and loss are negligible, we review previous works on the optimal strategies for minimal-error retrieving of information (ambiguous quantum reading) and perfect but probabilistic retrieving of information (unambiguous quantum reading). The optimal strategies largely overcome the optimal coherent protocols (reminiscent of common CD readers), further allowing for perfect discrimination. Experimental proposals for optical implementations of optimal quantum reading are provided.

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